The sensitivity analysis in pyPowsybl¶

In this notebook, you will learn how to run a sensitivity analysis on a network using pypowsybl.

This type of analysis allows to study the sensitivity of state variables to small fluctuations in a variable. As an example, we can examine the impact of varying the active power of a generator in the active power flow on the branches surrounding this generator.

It is also possible to calculate Power Transfer Distribution Factors (PTDF). In this case, zones are defined and the effect of the variation of the net position of a zone on a branch between this zone and another one.

The first step is to install pypowsybl and import the library.

In [ ]:

pip install pypowsybl

In [1]:

import pypowsybl as pp

We will consider the six buses example network in this notebook. It is available directly in the pyPowsybl library.

In [2]:

n6 = pp.network.create_metrix_tutorial_six_buses_network()

By drawing the network area diagram, you can get a better understanding of the substations and branches in the network.

In [3]:

n6.get_network_area_diagram()

Out[3]:

NE_poste

</td> <td>380.0 kV / -0.0°</td> </tr> </table>

</foreignObject> <foreignObject id="2-textnode" y="-17.17" x="-201.17" height="1" width="1">

NO_poste

</td> <td>380.0 kV / 0.0°</td> </tr> </table>

</foreignObject> <foreignObject id="4-textnode" y="-364.59" x="-309.07" height="1" width="1">

N_poste

</td> <td>380.0 kV / -0.0°</td> </tr> </table>

</foreignObject> <foreignObject id="6-textnode" y="49.88" x="365.98" height="1" width="1">

SE_poste

</td> <td>380.0 kV / -0.1°</td> </tr> </table>

</foreignObject> <foreignObject id="8-textnode" y="281.85" x="82.56" height="1" width="1">

SO_poste

</td> <td>380.0 kV / 0.0°</td> </tr> </table>

</foreignObject> <foreignObject id="10-textnode" y="436.99" x="408.62" height="1" width="1">

S_poste

</td> <td>380.0 kV / -0.0°</td> </tr> </table>

</foreignObject>

1 - The sensitivity analysis¶

To perform a sensitivity analysis, the first thing to do is define the “factors” you want to compute. What we call a factor is the impact of a small variation of a variable, typically the active power injection of a generator, a load or a phase shifter, on a function, typically the active power flow on a branch.

To make the definition of those factors easier, pypowsybl provides a method to define the variables (injection, phase shifter) through their ids (variables_ids) and the functions through the branch ids (branches_ids). We obtain a matrix of sensitivities as a result. First, let's create the analysis:

In [4]:

analysis = pp.sensitivity.create_dc_analysis()

Now let's create the factors. We are going to study the impact on the active power flow of S_SO_1 and S_SO_2 of a variation of the active power injection of the generator SE_G. S_SO_1 and S_SO_2 are the two lines connecting the substations S and SO and SE_G is the generator in the substation SE. To define these factors, you just need to give their IDs to the creation function like this:

In [5]:

analysis.add_branch_flow_factor_matrix(branches_ids=['S_SO_1', 'S_SO_2'], variables_ids=['SE_G'])

Now you can run the analysis with:

In [6]:

result = analysis.run(n6)

Let's examine the results of the sensitivity analysis. First, we can have a look at the reference matrix. It contains the flows on the previously defined branches according to the load flow.

In [7]:

result.get_reference_matrix()

Out[7]:

	S_SO_1	S_SO_2
reference_values	-120.433341	-120.433341

Now, we can look at the sensitivity matrix, which shows how the active power flow of the two lines changes when the generator's active power changes.

In [8]:

result.get_sensitivity_matrix()

Out[8]:

	S_SO_1	S_SO_2
SE_G	0.26087	0.26087

An increase of 1 MW on generator SE_G has the effect of increasing the active power flow from side 1 to side 2 by 0.26 MW on the lines S_SO_1 and S_SO_2.

2 - Zone to zone sensitivity: PTDF computation¶

This zone-to-zone sensitivity feature is also known as Power Transfer Distribution Factor, or PTDF for short.

Now, imagine that the node SE, is in Italy and the other nodes are in France. We can update the TSO and country field of the substations.

In [9]:

n6b = pp.network.create_metrix_tutorial_six_buses_network()
n6b.update_substations(id=['SE'], TSO=['Terna'], country=['IT'])
n6b.update_substations(id=['NO', 'S', 'SO', 'N'], TSO=['RTE', 'RTE', 'RTE', 'RTE'], country=['FR', 'FR', 'FR', 'FR'])

We can run a load flow:

In [10]:

pp.loadflow.run_dc(n6b)

Out[10]:

[ComponentResult(connected_component_num=0, synchronous_component_num=0, status=CONVERGED, status_text=Converged, iteration_count=0, reference_bus_id='NE_poste_0', slack_bus_results=[SlackBusResult(id='NE_poste_0', active_power_mismatch=4.440892098500626e-14)], distributed_active_power=nan)]

In the dataframe with the substation information, the TSO and country columns are now filled.

In [11]:

n6b.get_substations()

Out[11]:

	TSO	country
id
NO	RTE	FR
S	RTE	FR
SO	RTE	FR
SE	Terna	IT
N	RTE	FR

Now we can create two zones for the sensitivity analysis: one for France and one for Italy:

In [12]:

zone_fr = pp.sensitivity.create_country_zone(n6b, 'FR')
zone_it = pp.sensitivity.create_country_zone(n6b, 'IT')

<enum 'ZoneKeyType'>
<enum 'ZoneKeyType'>
True
<enum 'ZoneKeyType'>
<enum 'ZoneKeyType'>
True

We can examine the shift keys for the zone representing France. They're linked to the active power setpoint of the generators:

In [13]:

zone_fr.shift_keys_by_injections_ids

Out[13]:

{'SO_G1': 480.0, 'SO_G2': 480.0, 'N_G': 0.0}

Let's create the analysis and set the zones to the two we previously declared.

In [14]:

params = pp.loadflow.Parameters(distributed_slack=False)
sa = pp.sensitivity.create_dc_analysis()
sa.set_zones([zone_fr, zone_it])

And we can create the factor matrix again. This time, we're looking at how changing the net position of the two zones, FR and IT, affects the active power flow of the lines S_SE_1 and S_SE_2.

In [15]:

sa.add_branch_flow_factor_matrix(branches_ids=['S_SE_1', 'S_SE_2'], variables_ids=['FR', 'IT'])

We can run the analysis and get the sensitivity matrix.

In [16]:

ptdf_results = sa.run(n6b, params)
m1 = ptdf_results.get_branch_flows_sensitivity_matrix()
m1

Out[16]:

	S_SE_1	S_SE_2
FR	0.2	0.2
IT	-0.1	-0.1

Transferring 1 MW of active power from the zone FR to the zone IT will cause a 0.3 MW shift on border line S_SE_1.

Let’s obtain that directly. After running a sensitivity analysis to figure out the best zones, we can request a FR zone to slack sensitivity, a FR to IT zone to zone sensitivity, an IT to FR zone to zone sensitivity, and an IT zone to slack sensitivity on all the border lines S_SE_1, S_SE_2, SE_NE_1 and SE_NE_2.

In [17]:

sa = pp.sensitivity.create_dc_analysis()
sa.set_zones([zone_fr, zone_it])
sa.add_branch_flow_factor_matrix(branches_ids=['S_SE_1', 'S_SE_2', 'SE_NE_1', 'SE_NE_2'], variables_ids=['FR', ('FR', 'IT'), ('IT', 'FR'), 'IT'])
ptdf_result = sa.run(n6b, params)

In [18]:

m2 = ptdf_result.get_branch_flows_sensitivity_matrix()
m2

Out[18]:

	S_SE_1	S_SE_2	SE_NE_1	SE_NE_2
FR	0.2	0.2	0.2	0.2
FR -> IT	0.3	0.3	-0.2	-0.2
IT -> FR	-0.3	-0.3	0.2	0.2
IT	-0.1	-0.1	0.4	0.4

We can see that:

an increase of 1 MW on the FR zone net position leads to an increase of 0.2 MW on the flow of all the border lines.
moving the flow of 1 MW from FR to IT leads to an increase of 0.3 MW on the flow of lines S_SE_1 and S_SE_2 and a decrease of 0.2 MW on the flow of lines SE_NE_1 and SE_NE_2.
moving the flow of 1 MW from IT to FR leads to a decrease of 0.3 MW on the flow of lines S_SE_1 and S_SE_2 and an increase of 0.2 MW on the flow of lines SE_NE_1 and SE_NE_2.
an increase of 1 MW on the IT zone net position leads to a decrease of 0.1 MW on the flow of lines S_SE_1 and S_SE_2 and an increase of 0.4 MW on the flow of lines SE_NE_1 and SE_NE_2.